Details

analyze56.0ms (1.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	12.5%	87.5%	0
0%	12.5%	87.5%	1
0%	12.5%	87.5%	2
3.1%	9.3%	87.5%	3
3.1%	6.2%	90.7%	4
4.7%	4.7%	90.7%	5
4.7%	3.5%	91.8%	6
5.6%	2.5%	91.8%	7
5.9%	1.8%	92.3%	8
6.4%	1.3%	92.3%	9
6.6%	0.9%	92.5%	10
6.8%	0.6%	92.5%	11
6.9%	0.5%	92.6%	12
7%	0.3%	92.6%	13
7.1%	0.2%	92.7%	14

Compiler

Compiled 24 to 17 computations (29.2% saved)

sample313.0ms (8.9%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
6.0ms	257×	pre	128	true
0.0ms	1×	body	128	invalid

Compiler

Compiled 39 to 28 computations (28.2% saved)

simplify119.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

1186×	`fma-def_binary64`
913×	`fma-neg_binary64`
520×	`distribute-rgt-in_binary64`
481×	`div-sub_binary64`
441×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	20	16
2	39	14
3	78	14
4	233	14
5	529	14
6	976	14
7	1686	14
8	1746	14
9	1952	14
10	2334	14
11	2818	14
12	3104	14
13	4560	14
14	4195	14
15	4799	14

prune4.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
▶	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

Compiler

Compiled 73 to 49 computations (32.9% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 m (-.f64 1 m))
✓	0.0b	(/.f64 (*.f64 m (-.f64 1 m)) v)
✓	0.2b	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)

series27.0ms (0.8%)

Counts

3 → 56

Calls

3 calls:

14.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
10.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
2.0ms	(*.f64 m (-.f64 1 m))

rewrite30.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
29×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

3 → 102

Calls

3 calls:

10.0ms	(.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1) m)
7.0ms	(/.f64 (*.f64 m (-.f64 1 m)) v)
6.0ms	(*.f64 m (-.f64 1 m))

simplify86.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

519×	`fma-def_binary64`
423×	`distribute-rgt-in_binary64`
385×	`distribute-lft-in_binary64`
346×	`associate-/l/_binary64`
288×	`fma-neg_binary64`

Counts

158 → 169

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	178	2119
1	364	1923
2	1597	1729
3	4495	1728
4	4950	1728

prune169.0ms (4.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	162	7	169
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	163	8	171

Error

Counts

171 → 8

Alt Table

Status	Error	Program
	7.3b	(.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v))) 1) m)
	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	12.3b	(/.f64 (.f64 (-.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (.f64 1 1)) m) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
	0.5b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
▶	0.2b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
	33.2b	(.f64 (sqrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (*.f64 m (sqrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
	32.8b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)

Compiler

Compiled 3455 to 1947 computations (43.6% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 m (/.f64 v (-.f64 1 m)))
✓	0.2b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)

series29.0ms (0.8%)

Counts

2 → 48

Calls

2 calls:

15.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))
14.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)

rewrite48.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

153×	`times-frac_binary64`
128×	`add-sqr-sqrt_binary64`
110×	`*-un-lft-identity_binary64`
69×	`add-cube-cbrt_binary64`
30×	`difference-of-squares_binary64`

Counts

2 → 148

Calls

2 calls:

25.0ms	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
9.0ms	(/.f64 m (/.f64 v (-.f64 1 m)))

simplify286.0ms (8.1%)

Algorithm

1×	egg-herbie

Rules

692×	`times-frac_binary64`
512×	`associate-/r/_binary64`
400×	`distribute-rgt-in_binary64`
378×	`distribute-lft-in_binary64`
275×	`fma-def_binary64`

Counts

196 → 237

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	260	3891
1	556	3655
2	2044	3584
3	4576	3584
4	5018	3584

prune268.0ms (7.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	237	0	237
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	237	8	245

Error

Counts

245 → 8

Alt Table

Status	Error	Program
	7.3b	(.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v)) (sqrt.f64 (/.f64 (.f64 m (-.f64 1 m)) v))) 1) m)
	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	12.3b	(/.f64 (.f64 (-.f64 (.f64 (/.f64 (.f64 m (-.f64 1 m)) v) (/.f64 (.f64 m (-.f64 1 m)) v)) (.f64 1 1)) m) (+.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1))
	0.5b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
✓	0.2b	(*.f64 (-.f64 (/.f64 m (/.f64 v (-.f64 1 m))) 1) m)
	33.2b	(.f64 (sqrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (*.f64 m (sqrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
▶	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
	32.8b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)

Compiler

Compiled 5247 to 3021 computations (42.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 m (-.f64 1 m))
✓	0.0b	(/.f64 v (*.f64 m (-.f64 1 m)))
✓	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
✓	0.3b	(/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m))))

series55.0ms (1.6%)

Counts

3 → 68

Calls

3 calls:

30.0ms	(/.f64 v (*.f64 m (-.f64 1 m)))
14.0ms	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
10.0ms	(/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m))))

rewrite41.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`times-frac_binary64`
42×	`add-sqr-sqrt_binary64`
34×	`*-un-lft-identity_binary64`
31×	`add-exp-log_binary64`
25×	`add-cube-cbrt_binary64`

Counts

3 → 124

Calls

3 calls:

18.0ms	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
8.0ms	(/.f64 1 (/.f64 v (*.f64 m (-.f64 1 m))))
5.0ms	(/.f64 v (*.f64 m (-.f64 1 m)))

simplify107.0ms (3%)

Algorithm

1×	egg-herbie

Rules

885×	`times-frac_binary64`
359×	`distribute-rgt-in_binary64`
334×	`fma-neg_binary64`
327×	`distribute-lft-in_binary64`
273×	`associate-/r/_binary64`

Counts

192 → 199

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	189	3188
1	412	2804
2	1397	2683
3	4268	2683
4	5165	2683

prune232.0ms (6.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	268	2	270
Fresh	2	4	6
Picked	0	1	1
Done	1	0	1
Total	271	7	278

Error

Counts

278 → 7

Alt Table

Status	Error	Program
▶	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	0.4b	(.f64 (-.f64 (.f64 (/.f64 1 (/.f64 (sqrt.f64 v) m)) (/.f64 1 (/.f64 (sqrt.f64 v) (-.f64 1 m)))) 1) m)
	0.5b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
	33.2b	(.f64 (sqrt.f64 (-.f64 (/.f64 (.f64 m (-.f64 1 m)) v) 1)) (*.f64 m (sqrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1))))
✓	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
	32.8b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)
	7.7b	(-.f64 (*.f64 (/.f64 m v) m) m)

Compiler

Compiled 5789 to 3727 computations (35.6% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 1 m) v)
✓	0.2b	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)
✓	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))

series27.0ms (0.8%)

Counts

3 → 64

Calls

3 calls:

13.0ms	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
8.0ms	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)
6.0ms	(/.f64 (-.f64 1 m) v)

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
28×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
16×	`add-cube-cbrt_binary64`
8×	`difference-of-squares_binary64`

Counts

3 → 76

Calls

3 calls:

5.0ms	(/.f64 (-.f64 1 m) v)
4.0ms	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
0.0ms	(fma.f64 m (/.f64 (-.f64 1 m) v) -1)

simplify100.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

562×	`fma-neg_binary64`
332×	`distribute-rgt-neg-out_binary64`
308×	`associate-l_binary64`
305×	`div-sub_binary64`
264×	`exp-prod_binary64`

Counts

140 → 127

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	135	2018
1	285	1760
2	745	1726
3	2553	1726
4	4478	1726
5	4976	1726

prune144.0ms (4.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	2	3	5
Picked	0	1	1
Done	0	1	1
Total	127	7	134

Error

Counts

134 → 7

Alt Table

Status	Error	Program
✓	0.2b	(*.f64 m (fma.f64 m (/.f64 (-.f64 1 m) v) -1))
	0.2b	(+.f64 (.f64 m (/.f64 (-.f64 m (.f64 m m)) v)) (neg.f64 m))
	0.4b	(.f64 (-.f64 (.f64 (/.f64 1 (/.f64 (sqrt.f64 v) m)) (/.f64 1 (/.f64 (sqrt.f64 v) (-.f64 1 m)))) 1) m)
	0.5b	(.f64 (.f64 (-.f64 (/.f64 (*.f64 m (-.f64 1 m)) v) 1) (sqrt.f64 m)) (sqrt.f64 m))
	33.1b	(.f64 (.f64 m (sqrt.f64 (fma.f64 (/.f64 m v) (-.f64 1 m) -1))) (sqrt.f64 (fma.f64 m (/.f64 (-.f64 1 m) v) -1)))
✓	0.2b	(.f64 (-.f64 (/.f64 1 (/.f64 v (.f64 m (-.f64 1 m)))) 1) m)
	32.8b	(/.f64 (*.f64 (-.f64 m (pow.f64 m 2)) m) v)

Compiler

Compiled 2085 to 1259 computations (39.6% saved)

regimes477.0ms (13.5%)

Accuracy

Total 0.2b remaining (90%)

Threshold costs 0.2b (90%)

Counts

147 → 1

Compiler

Compiled 8151 to 5530 computations (32.2% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`*-commutative_binary64`
3×	`sub-neg_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	20	16
2	25	16
3	28	16
4	29	16
5	29	16

end0.0ms (0%)

Compiler: Compiled 13 to 7 computations (46.2% saved)

sample878.0ms (24.8%)

Algorithm

1×

intervals

Results

323.0ms	8000×	body	128	valid
176.0ms	8054×	pre	128	true
2.0ms	54×	body	128	invalid

Compiler

Compiled 152 to 102 computations (32.9% saved)

Details

analyze56.0ms (1.6%)

sample313.0ms (8.9%)

simplify119.0ms (3.4%)

prune4.0ms (0.1%)

localize7.0ms (0.2%)

series27.0ms (0.8%)

rewrite30.0ms (0.8%)

simplify86.0ms (2.4%)

prune169.0ms (4.8%)

localize7.0ms (0.2%)

series29.0ms (0.8%)

rewrite48.0ms (1.4%)

simplify286.0ms (8.1%)

prune268.0ms (7.6%)

localize9.0ms (0.2%)

series55.0ms (1.6%)

rewrite41.0ms (1.2%)

simplify107.0ms (3%)

prune232.0ms (6.6%)

localize6.0ms (0.2%)

series27.0ms (0.8%)

rewrite13.0ms (0.4%)

simplify100.0ms (2.8%)

prune144.0ms (4.1%)

regimes477.0ms (13.5%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample878.0ms (24.8%)

Profiling